Buddhism and China have a very long history, despite the blip during the Cultural Revolution, hence it is natural for China to be more inclined towards Buddhism. Especially as Tibet is now a part of China, Tibetan Buddhism will be more prevalent, and there are already Tibetan Buddhist elements throughout China, such as the Lama Tsongkhapa statue in Yong He Gung temple in Beijing.
Whatever the reasons China has for supporting Dorje Shugden practitioners, i think that they are continuing to do so because they see that Dorje Shugden lamas are willing to work with the Chinese authorities and all the Chinese authorities wish for is a stable environment for its peoples. Dorje Shugden lamas are also willing to work with the Chinese because they can see that if they work together with the authorities as opposed to against them, it will allow more freedom for Dorje Shugden practitioners, even to the extent of Dorje Shugden lamas being allowed to travel internationally. It is a win-win situation. For the Dorje Shugden lamas, the more exposure of the people to Dorje Shugden means the more exposure to Manjushri and that people will have Dharma seeds planted, whatever the reasons why the Chinese are propitiating Dorje Shugden. Even if the reasons are secular, the eventual result will be spiritual.